(4+w)(5w+6)=30

Solution for (4+w)(5w+6)=30 equation:

(4+w)(5w+6)=30

We move all terms to the left:

(4+w)(5w+6)-(30)=0

We add all the numbers together, and all the variables

(w+4)(5w+6)-30=0

We multiply parentheses ..

(+5w^2+6w+20w+24)-30=0

We get rid of parentheses

5w^2+6w+20w+24-30=0

We add all the numbers together, and all the variables

5w^2+26w-6=0

a = 5; b = 26; c = -6;
Δ = b2-4ac
Δ = 262-4·5·(-6)
Δ = 796
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{796}=\sqrt{4*199}=\sqrt{4}*\sqrt{199}=2\sqrt{199}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{199}}{2*5}=\frac{-26-2\sqrt{199}}{10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{199}}{2*5}=\frac{-26+2\sqrt{199}}{10}
$